Edwina Aylward

Hello! I am a third year PhD student at University College London under the supervision of Vladimir Dokchitser.

I am interested in algebraic number theory and arithmetic geometry. More specifically, my research concerns elliptic and hyperelliptic curves, the Birch and Swinnerton-Dyer conjecture, and parity conjectures.

Previously, I completed my undergraduate studies at Trinity College Dublin, and the Part III masters course at Trinity College, Cambridge. A copy of my CV is here.

Preprints

• Tamagawa numbers and positive rank of elliptic curves (April 2025).

Talks

• Tate modules of hyperelliptic curves (November 2025, Genus 2 and hyperelliptic curves study group, UCL)

• p-parity conjecture for twists of hyperelliptic curves by Artin representations (November 2025, Manchester number theory seminar, University of Manchester)

• l-parity results for abelian varieties over global function fields (November 2025, London junior number theory seminar, KCL)

• Ranks of elliptic curves (November 2025, Postgraduate seminar, UCL)

• Reduction types of genus 2 curves (July 2025, LuCaNT 2025, Providence, RI)

• Reduction types of genus 2 curves (April 2025, WINGs 2025)

• Elliptic curves with positive rank (March 2025, Elliptic curves in the Cotswolds meeting, Stonehouse)

• Explicit regular models of hyperelliptic curves (March 2025, Models of Curves and Arithmetic Applications study group, UCL)

• Extended Weyl group and affine Dynkin diagrams (November 2024, Bruhat-Tits theory study group, KCL)

• Artin's primitive root conjecture (November 2024, 'Open problems in number theory' study group, UCL)

• Rank predictions: parity vs. L-value approaches (November 2024, Junior number theory seminar, University of Warwick)

• A survey of the Inverse Galois Problem (October 2024, London junior number theory seminar, KCL)

• Artin formalism and BSD (August 2024, YRANT VI, University of Oxford)

• Introduction to Etale cohomology (May 2024, Galois cohomology study group, KCL)

• Ray class fields (April 2024, Class field theory study group, UCL)

• Modularity theorem and Diophantine equations (October 2023, 10 minute presentations, UCL)

Other writings

• Simple wild parameters and simple supercuspidal representations (June 2024, LSGNT mini-project 2, supervised by Beth Romano)

• Artin formalism and BSD (March 2024, LSGNT mini-project 1, joint with Albert Lopez-Bruch and supervised by Vladimir Dokchitser)

• The modularity theorem and the modular approach (May 2023, Part III essay)

• Steenrod squares and the Steenrod algebra (May 2022, final year undergraduate project)

(Co-)Organisation

• Women in number theory and geometry spring retreat (WINGs): 13-16 April 2026.
• London junior number theory seminar: 2024-2025.
• Elliptic Curves in the Cotswolds meeting: 03-04 March 2025.

Contact

You can contact me at firstname.lastname.23@ucl.ac.uk.